JPH0216846B2 - - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a nonlinear arithmetic circuit that provides a nonlinear relationship between an input signal and an output signal suitable for correcting nonlinear errors of thermocouples and the like.

Generally, in process measurement control, it is often necessary to linearize a non-linear signal or, conversely, to non-linearize a linear signal. In such cases, non-linear calculation circuits are used.

Conventionally, multipliers using logarithmic amplifiers or differential amplifiers have been used to obtain quadratic function signals of input signals, but the circuits are complex and require transistor pairs with well-matched characteristics, making stable It was difficult to guarantee operation. Therefore, monolithic IC multipliers are now commercially available.
Most multipliers rely on this IC multiplier. However, this IC multiplier had the drawback of being expensive.

On the other hand, methods for realizing a non-linear arithmetic circuit capable of generating higher-order function signals include a method using a plurality of broken line approximations and a method using higher-order function approximation.

In order to obtain high accuracy with the former method, the number of broken lines increases and the bending point and its slope must be adjusted for each broken line, which is extremely troublesome. As for the latter method, a cubic function approximation method using a plurality of multipliers has been proposed, but this method has the disadvantage that the circuit configuration is complicated and expensive.

The purpose of the present invention is to
It is an object of the present invention to provide a nonlinear arithmetic circuit that can obtain a high-order function of a thermocouple with excellent characteristics even with a simple circuit configuration.

The present invention utilizes the fact that the DC component of the difference signal between the input signal and the triangular wave is a quadratic function signal of the input signal, and its feature is to obtain the difference signal between the input signal from the thermocouple and the triangular wave. A common set includes an operational amplifier and a smoothing circuit that takes out the direct current component of the difference signal, and three operational amplifiers that add and subtract the output of the common smoothing circuit and the input signal and a constant voltage. and 0% of the input signal, respectively.
a first quadratic function signal that becomes zero at 100% time and 100%;
a second quadratic function signal that becomes zero at 0% and 50% of the input signal, and a second quadratic function signal that becomes zero at 50% and 100% of the input signal;
A fourth operational amplifier generates three quadratic function signals, the third quadratic function signal being zero at times, and combines the first, second and third quadratic function signals with the input signal. By compositing, an output signal that approximates a high-order function is obtained.

Hereinafter, the present invention will be explained in detail based on the drawings.

FIG. 1 is a circuit connection diagram showing an embodiment of the present invention that generates a quadratic function signal, and FIG. 2 is a diagram showing a triangular wave used in the present invention and its operation. In FIG. 1, 1 is an input terminal, 2 is a triangular wave generator, 3 is an output terminal, and 4 is an operational amplifier. _R1 to _R7 are resistances, C
is a capacitor, and D ₁ and D ₂ are rectifiers, such as diodes. The triangular wave output from the triangular wave generator 2 has a period T and a peak value, as shown by the solid line in Figure 2.
Let E be ₀ .

In such a configuration, when the input signal V _io is applied, for example, if resistors R ₁ to R ₅ are all of the same value for simplicity, the output of the ideal diode composed of the operational amplifier 4 _E1 is
This is the shaded area in FIG. Next, _R7 and the capacitor C constitute a smoothing circuit, and the time constant C· _R7 is selected to be sufficiently larger than the period T of the triangular wave. Therefore, the output _Vput is the DC component of _E1 , that is, the average value, and has the value shown below.

V _put =∫ ^1/0 E ₁ dt/T = 1/2×T/E ₀ × (E ₀ −V _io )×(E ₀ −V _io ) _/
T = 1/2E ₀ (E ₀ −V _io ) ² = 1/2E ₀ V ² _io −V _io +E ₀ /2…(1) In this way, the output V _put is a quadratic function signal of the input signal V _io It's summery.

Moreover, by further performing calculations on V _put and manipulating the linear term and zero-order term, various quadratic function signals can be obtained. An example of this is shown in FIG.

In FIG. 3, 1 is an input terminal, 2 is a triangular wave generator, 3 is an output terminal, 4 and 5 are operational amplifiers, and 6 is a constant voltage source whose voltage is _Vb . _R1 to _R3 are resistances,
VR ₁ is a variable resistor, C is a capacitor, and D ₁ and D ₂ are rectifiers, such as diodes. Here, E ₂ is the same voltage as V _put in FIG. 1, and E ₂ = 1/2E ₀ V _io ² −V _io +E ₀ /2 (2). In addition, in order to balance the impedance seen from the input terminal of the operational amplifier 5 and make the calculation 1:1, the variable resistor VR ₁ is selected to be sufficiently smaller than the resistor R ₁ , and the output resistance of the signal E ₂ is set to R ₃ . Therefore, R ₃ =R ₁ /2.

By applying V _a and V _b here, the signal
You can manipulate the first-order and zero-order terms of E ₂ ,
Various quadratic function signals can be obtained.

For example, if you want to obtain the signal V _{put =} 1/2E ₀・V _io ² at V put, set V _a = V _io and V _b = E ₀ /2, then V _put = E ₂ + V _a −E ₀ /2 = It can be obtained as follows: 1/2E ₀ V _io ² −V _i +E ₀ /2+V _io −E ₀ /2 = 1/2E ₀ V _io ² (3).

A feature of the circuit of this embodiment is that the accuracy is determined only by the peak value E ₀ of the triangular wave and the characteristics of the ideal diode. As long as only the peak value E ₀ of the triangular wave is stable, if the time constant of the smoothing circuit is made large, there will be no problem even if the period T is out of order. For the ideal diode, an operational amplifier with a faster response than the period T of the triangular wave and a diode with less reverse leakage current may be prepared. By doing so, a highly accurate and stable quadratic function generating circuit can be obtained.

Next, FIGS. 4 to 13 show an example of the case where the nonlinear arithmetic unit according to the present invention corrects the nonlinear error of a thermocouple.
This will be explained using figures. Correction of non-linear errors is performed by passing the signal through a circuit having non-linearity opposite to that of the non-linear errors. This circuit is, in other words, a nonlinear arithmetic circuit.

Looking at the interpolation formula, the electromotive force with respect to the temperature of the thermocouple is a 7th to 8th order function. Here, the R-type thermocouple, which has the largest nonlinear error and is difficult to correct, will be explained as an example.

In FIG. 4, the nonlinear error of the thermoelectromotive force with respect to the temperature of the R-type thermocouple from 0° C. to 600° C. is shown by a solid line.

This nonlinear error is the first quadratic function signal that becomes zero at 0% and 100% of the input signal.
If an approximation is made so that the non-linear error becomes zero at 50% (dashed line in Figure 1), the remaining error will be as shown in Figure 5.

Next, the nonlinear error in Figure 5 is divided into a second quadratic function signal that becomes zero at 0% and 50% of the input signal, and a third quadratic function signal that becomes zero at 50% and 100% of the input signal. Function signal at 25% and 75% of input signal respectively
If the approximation is made so that the error becomes zero at % (dashed line in Figure 2), the remaining error will be ± as shown in Figure 3.
It will be less than 0.3%.

These quadratic function signals approximate only the nonlinear error, and by combining these quadratic function signals and the input signal and feeding back, the nonlinearity inverse to the nonlinear error can be obtained. It becomes a non-linear error correction circuit for R-type thermocouples from 0℃ to 600℃,
Nonlinear errors can be corrected to less than ±0.3%.

As described above, since good nonlinear error correction can be performed for the R-type thermocouple with the largest nonlinear error, sufficient nonlinear error correction can be performed for all other thermocouples as well. Examples of this are shown in FIGS. 7-9.

FIG. 10 shows an example of three quadratic function signals using the nonlinear arithmetic unit of the present invention. In the present invention, these three
The magnitude and polarity of the two quadratic function signals are not limited, but are set depending on the object to be subjected to nonlinear calculation.
It is a choice.

In addition, in the above example of nonlinear error correction for thermocouples,
Although the nonlinear arithmetic circuit of the present invention is included in the feedback circuit, the present invention is not limited to this, and may be used as a feedback circuit. However, in the case of non-linear error correction for thermocouples, it is better to include them in a feedback circuit than to use them as feed-forwards, as the overall correction accuracy is higher and error calculations are easier. In general, when the input signal is small and the error is large, the feedback type provides good results, and vice versa, the feedback type provides good results.

FIG. 8 is a circuit connection diagram showing an embodiment of the present invention for obtaining such a function signal. In FIG. 8, 7 is an input terminal, 8 is a triangular wave generation circuit with an output _DT , 9 is a constant voltage source with an output of V ₃ , 10 is an output terminal,
11 to 13 are switches for selecting addition or subtraction;
14 to 19 are operational amplifiers, R ₁ to R ₁₅ are resistors, VR ₁
~VR ₃ is a variable resistor, C ₁ and C ₂ are capacitors, D ₁
~ _D6 is a rectifier, for example a diode. 12th
The figure is a diagram for explaining the operation of this embodiment, and the triangular wave V _T used here has a period T and a peak value mark. FIG. 13 shows how to use the nonlinear arithmetic unit shown in FIG. 11. The operation will be explained below.

First, when the input signal V _io is applied to the input terminal 7,
The output E _T of the operational amplifier 14 is the shaded portion in FIG. R ₃ and C ₁ constitute a smoothing circuit, and the time constant C ₁ R ₃ is the period T of the triangular wave ET.
It is chosen to be sufficiently large compared to . Operational amplifier 14
is a buffer for impedance conversion.
Therefore, the output E ₀ of the operational amplifier is the DC component of _ET , that is, the average value, and E ₀ is expressed as follows.

E ₀ =∫ ^T / ₀ E _T dt / T = 1/2E _P (V _io −E _P ) ² = 1/2E _P (V _io ² −2V _io E _P +E _P ² ) …(4) Like this E ₀ becomes a quadratic function signal of the input signal V _io . Next, by manipulating the first-order and zero-order terms of the signal E ₀ using operational amplifiers 16, 17, and 18, the required quadratic function signal can be obtained. Now, correct the non-linear error of the thermocouple from 0 to 4.
(V) signal level. Triangle wave E _T
The peak value E _P of must be larger than the input signal, so E _P =6 (V). Then, E ₀ =1/12 (V _io ² −12V _io +36) …(5). In addition, the first quadratic function signal E ₁ which becomes zero at 0% and 100% of the input signal,
% and the second quadratic function signal E ₂ which becomes zero at 50%,
The third quadratic function signal _E3 , which becomes zero at 50% and 100% of the input signal, is expressed as follows.

E ₁ = 1/12V _io (V _io -4) ...(6) E ₂ = 1/12V _io (V _io -2) ...(7) E ₃ = 1/12 (V _io -2) (V _io - 4) ...(8) To obtain the signal E ₁ , the operational amplifier 10 converts E ₀ to
Just subtract 36/12 (V) and add 8/12V _io . That is, E ₁ = E ₀ −3 + 8/12V _io = 1/12 (V _io ² −12V _io +36) −36/12 + 8/12V _io = 1/12 (V _io ² −4V _io ) = 1/12V _io ( V _io −4) …(9) Next, to obtain the signal E ₂ , the operational amplifier 11 converts E ₀
Just subtract 36/12 (V) from and add 10/12V _io . In addition, in order to remove unnecessary portions of this quadratic function signal, diodes D ₁ and D ₂ and a resistor R ₁ are included to form an ideal diode as is well known. Similarly, to obtain the signal E ₃ , the operational amplifier 12 subtracts 28/12 (V) from the signal E ₀ and adds 6/12V _io . This also constitutes an ideal diode to remove unnecessary parts. Here resistance R ₄ ~ _{R 15}
If is chosen sufficiently small compared to the resistor R ₁ , D ₁ = 2/3V _io , V ₂ = 5/6V _io , V ₃ = 1/2V _io D ₄ = 3 (V), V ₅ = 3 (V) , V ₆ = 7/3 (V), the quadratic function signals E ₁ , E ₂ ,
You can get _E3 .

By the way, if you set the numbers as above,
The absolute values of the extreme values of the quadratic function signals E ₁ , E ₂ , and E ₃ are 0.33 (V), 0.083 (V), and 0.083 (V), respectively.
Also, since the non-linear error of a thermocouple is at most 8%, for a 4 (V) span, it is 0.32 (V), and the correction by E ₂ and E ₃ is the remaining error once corrected by E ₁ . Since it is a correction, it is at most 2%, and 4
(V) Since it is 0.08 (V) for the span,
It can be seen that the above numerical settings are necessary and sufficient.

Next, the quadratic function signal is generated using variable resistors VR ₁ , VR ₂ , VR ₃
Multiply E ₁ , E ₂ , E ₃ by the coefficient and switch 11, 12,
By selecting addition or subtraction in step 13 and combining it with the input signal _Vio , the nonlinear arithmetic unit of the present invention is constructed. Variable resistors VR ₁ , VR ₂ , VR ₃ are R ₁
It is chosen to be sufficiently small compared to . Also, since it becomes a load on the ideal diode, it should be made small. Here, the capacitor _C2 is a capacitor for preventing oscillation when this non-linear arithmetic unit is included in the feedback circuit, and it is sufficient to insert about 100PF.

To adjust this nonlinear arithmetic unit, first select the polarity using switch 11, and when the input signal is 50%, use the variable resistance
Set VR ₁ to the specified output, then select the polarity with switches 12 and 13 so that the input signal is 25
%, 75%, variable resistors VR ₂ and VR ₃ are used to produce a predetermined output.

FIG. 13 shows a method of connecting the present nonlinear arithmetic unit and other circuits, taking as an example nonlinear error correction of a thermocouple. The symbols are the same as in FIG. 11, T is the temperature, E is the thermoelectromotive force, and k is the proportionality constant. FIG. 13a shows a feed forward type. First, the thermocouple changes from temperature T to thermoelectromotive force E.
It is a converter to This is expressed as T→E. In this case, if it is desired to obtain an output signal KT proportional to the temperature T, the present non-linear calculator may be used to calculate E→kT. However, the interpolation formula for thermocouples is T→E (E=f
(T)), it is extremely troublesome to calculate the error. FIG. 13b shows a feedback configuration that eliminates the above-mentioned drawbacks. In this case, the present non-linear calculation circuit calculates kT→E, so error calculation becomes easy.

However, in this embodiment, the feedback type is not limited, and the feedback type and the feedback type can be used depending on the purpose. In addition, this embodiment can of course be used not only for nonlinear error correction but also for active nonlinearization, and since it uses a quadratic function signal, it can also be easily used with a square root calculator. Can be configured. Furthermore, the triangular wave E _T
Since it is possible to perform pulse width modulation using a photocoupler, it can be easily isolated using a photocoupler, etc., and a temperature converter can be constructed by bringing a low input amplifier to the first stage.

According to this embodiment, there are the following effects. In other words, once the quadratic function signal is set, 3
Adjustment is easy because a wide variety of nonlinear calculations can be performed by adjusting one switch and three variable resistors.

In addition, when correcting non-linear errors of thermocouples,
± over all temperature ranges for all thermocouples
High accuracy as correction accuracy of 0.3% or less can be obtained.

Furthermore, unlike a non-linear arithmetic unit approximating a cubic function that uses a plurality of multipliers, the present invention does not use any multipliers, so it is relatively inexpensive.

Next, for example, in a K thermocouple of 200 DEG C. to 1000 DEG C., the nonlinear error can be corrected to below ±0.1% by the above method, as shown in FIGS. 14 to 16.

Note that FIG. 14 corresponds to FIG. 4, FIG. 15 corresponds to FIG. 5, and FIG. 16 corresponds to FIG. 6.
As described above, the basic principle of the nonlinear arithmetic circuit according to the present invention can be achieved by creating three quadratic function signals each having a different weight from an input signal, as shown in FIGS. 4 to 6, for example.

Next, FIG. 7 shows a configuration diagram of a nonlinear arithmetic circuit according to the present invention based on the above basic principle. In FIG. 17, 20 is an input terminal, 21 is an output terminal, 2
2 is a reference voltage source, 23 is a multiplier, and 24 to n are addition/subtraction calculators which have a rectifying function as required.

In operation, first, when the input signal V _i is applied to the input terminal 20, the output signal of the multiplier 23 becomes k ₀ V _i ² .
Here k ₀ is a proportionality constant. An addition/subtraction calculator 25 is connected between this signal k ₀ V _i ² , the input signal V _i , and the reference voltage V _s .
Addition and subtraction operations are performed with weights k _x , k _y , and k _{z ,} respectively, and the output signal V ₅ of the addition/subtraction calculator 25 is V ₅ =k _x・k ₀・V _i ² +k _y V _i +k _z Create a quadratic function signal that becomes V _s …(10). If the above equation is shown as a graph, it will be as shown in FIG. 18 or FIG.
The broken line portions in FIGS. 18 and 9 are removed and only the solid line portion is output. Next, addition/subtraction calculator 24
The output signals of the addition/subtraction operators 25 to n are
The non-linear calculation circuit of this embodiment can be constructed by adding and subtracting V ₆ , V ₇ , V ₈ , . . . _Vo together with the input signal _Vi . FIG. 20 is a specific circuit configuration diagram when the nonlinear calculation circuit according to the present invention is used for nonlinear error correction of thermocouples. Figure 21 shows the second
2 shows a quadratic function signal used to explain the diagram.

In Figure 20, the same parts as in Figure 17 have the same symbols. 31 to 34 are operational amplifiers;
D ₁ and D ₂ are rectifiers, such as diodes, for providing rectification to the addition/subtraction calculators 26 and 27. SW ₁ to _{SW 3} are switches for selecting addition or subtraction, and resistors R ₁ to _{R 7} are resistors, and R ₂ to R ₇ are selected to be sufficiently smaller than R ₁ . VR ₁ to _{VR 3} are variable resistors used to weight the quadratic function signals V ₆ , V ₇ , and V ₈ , and are also selected to be sufficiently smaller than the resistor R ₁ .

The signals handled in process measurement control are 1V to 5V.
voltage signal or 4mA to 20mA current signal. In order to facilitate conversion into these signals, nonlinear calculations are performed in the signal range of 0 to 4 V in this case. There are three quadratic function signals, the first quadratic function signal is a quadratic function signal that becomes zero at 0% and 100% of the input signal, and the second quadratic function signal is at 0% and 50% of the input signal. A quadratic function signal that sometimes becomes zero, the third
Let the quadratic function signal be a quadratic function signal that becomes zero at 50% and 100% of the input signal. Furthermore, since the non-linear error of the thermocouple is at most 8%, the absolute value of the extreme value of the first quadratic function signal only needs to be 0.32V, and in this case it is set to 0.4V. The remaining nonlinear error approximated by the first quadratic function signal is at most 1.5%.
Therefore, the absolute value of the extreme value of the second and third quadratic function signals only needs to be 0.06V, and in this case, it is set to 0.1V. Here, if the first quadratic function signal is V ₆ , the second quadratic function signal is V ₇ , and the third quadratic function signal is V ₈ , then V ₆ , V ₇ , and V ₈ are the 11th quadratic function signal. It will look like the figure.
Also, if expressed as a formula, it becomes as follows.

V ₆ = 1/10V _i (V _i −4) …(11) V ₇ = 1/10V _i (V _i −2) (V ₇ ≦0) …(12) V ₈ = 1/10 (V _i − 2) (V _i −4) (V ₈ ≦0) (13) Next, the operation of obtaining the above-mentioned quadratic function signal from the input signal V _i and performing nonlinear calculation will be described.

When the input signal V _i is applied to the input terminal 1, the output of the multiplier 23 becomes k ₀ V ₀ ² . Next, addition/subtraction calculator 25
Then, subtracting V ₁ from _Vi ² is performed, and the output is V ₆ V ₆ = k _{0 Vi} ² − V ₁ . Here, if k ₀ = ¹ ₁₀ and V ₁ ⁴ _{10 Vi} , then V ₆ = 1/10V _i ² -4/10V ¹ _i = 1/10V _i (V _i -4) ...(14) , a signal equivalent to equation (11) is obtained.

Next, the adder/subtractor 26 subtracts V ₂ from k ₀ V _i ² and connects the output terminal of the operational amplifier 32 and the feedback resistor.
A rectifier _D1 is inserted between _R1 to form an _ideal diode as is well known, and the _positive part _is removed and only ^the _{negative part} is _output . ) …(15) is obtained. Here, k ₀ = 1/10 and V ₂ = 2/10V _i , then V ₇ = 1/10V _i ² -2/10V _i = 1/10V _i (V _i -2) (V ₇ ≦0 )...(16), and a signal equivalent to equation (12) is obtained. The addition/subtraction calculator 27 subtracts V ₃ from k ₀ V _i ² and adds V _s to form an ideal diode in the same way as the addition/subtraction calculator 26, outputting only the negative part and giving V ₈ =k ₀ V _i ² −V ₃ +V _s (V ₈ ≦0) Signal V ₈ is obtained. Here, k ₀ = 1/10, V ₃ = 6/10V _i and V _s = 8/10 (V), then V ₈ = 1/10V _i ² −6/10V _i +8/10 = 1/ 10(V _i ² -6V _i +8) = 1/10(V _i -2) (V _i -4) (17) A signal equivalent to equation (13) is obtained. In this way, a desired quadratic function signal can be obtained.

Next, VR ₁ is applied to the quadratic function signals V ₆ , V ₇ , V ₈ ,
Add weight using VR ₂ and VR ₃ , select addition or subtraction using SW ₁ , SW ₂ , and SW ₃ , and add/subtract the input signal using adder/subtractor 5.
It operates by combining with V _i to obtain an output signal V ₀ .

To adjust the circuit of this example, first select the polarity with SW ₁ , adjust so that when the input signal is 50%, the specified output will be obtained with VR ₁ , and then change the polarity with SW ₂ and SW ₃ . When the selected input signal is 25% and 75% respectively
All you have to do is adjust VR ₂ and VR ₃ to achieve the desired output.

In the above embodiment, three quadratic function signals are used, but the present invention is not limited to this, and the number varies depending on nonlinearity and accuracy. Furthermore, it is naturally possible to not only correct non-linear errors but also actively make them non-linear.

According to this embodiment, a highly accurate non-linear arithmetic circuit can be configured with a single multiplier and a relatively simple circuit. A comparison between the nonlinear calculation circuit using three quadratic function signals in this embodiment and the conventional nonlinear calculation circuit using folded-edge approximation and cubic function approximation is as follows.

Once the quadratic function signal is set, adjustment is easy because various nonlinear calculations can be performed by adjusting three switches and three variable resistors.

Furthermore, when performing nonlinear error correction for an R-type thermocouple from 0°C to 600°C, the nonlinear calculation circuit of the present invention
The nonlinear error is less than ±0.3%, and the accuracy is high.
In contrast to the non-linear arithmetic circuit approximating a cubic function that uses a plurality of multipliers, the present invention requires only one multiplier, so it is inexpensive.

As explained above, according to the present invention, the operational amplifier that obtains the difference signal between the input signal from the thermocouple and the triangular wave, and the smoothing circuit that takes out the DC component of the difference signal are common. It is possible to realize a highly accurate non-linear arithmetic circuit with a simple circuit configuration as a whole without being affected by mismatches in elements and time constants.

[Brief explanation of drawings]

Figure 1 is a circuit diagram showing one embodiment of the present invention, Figure 2 is a circuit diagram showing an embodiment of the present invention.
The figure is a waveform diagram showing the embodiment of Fig. 1, and Fig. 3 is a waveform diagram showing the embodiment of Fig. 1.
4 to 10 are waveform diagrams for explaining the principle of one application example of the non-linear arithmetic circuit of the present invention, and FIG. 11 is a circuit diagram showing another embodiment of the present invention. The circuit diagram, FIGS. 12 to 13 are diagrams for explaining FIG. 11, and FIGS. 14 to 16 are nonlinear errors of R-type thermocouples and K-type thermocouples, and nonlinear calculations according to the present invention. A diagram showing a non-linear error after correction by a circuit, FIG. 17 is a basic circuit configuration diagram showing still another embodiment of the present invention, FIGS. 18 to 19 are diagrams explaining a quadratic function signal, FIG. 20 is a specific circuit diagram according to another embodiment of the present invention, and FIG. 21 is a diagram showing a quadratic function signal used in the present invention. 1...Input terminal, 2...Triangular wave generation circuit, 3...
...output terminal, 4...operational amplifier, _D1 , _D2 ...rectifier, _R1 to _R7 ...resistance, C...capacitor.

Claims (1)

[Claims] 1 A common set of an operational amplifier that obtains a difference signal between an input signal from a thermocouple and a triangular wave, and a smoothing circuit that extracts a DC component of the difference signal, and the output of the common smoothing circuit and the input It has three operational amplifiers that add and subtract between a signal and a constant voltage, and a first quadratic function signal that becomes zero at 0% and 100% of the input signal, and a first quadratic function signal that becomes zero at 0% and 100% of the input signal, respectively.
Generate three quadratic function signals, a second quadratic function signal that becomes zero at 50% and a third quadratic function signal that becomes zero at 50% and 100% of the input signal,
A fourth operational amplifier combines the first, second, and third quadratic function signals with the input signal to obtain an output signal that approximates a higher-order function. Arithmetic circuit.